Question

10sin^2x+11sinx-8=0

Answer 1

10sin²x+11sinx-8=0
sinx=a, |a|≤1
10a²+11a-8=0
D=11²-4*10*(-8)=121+320=441=$(pm21)^2$
$a_1= frac{-11-21}{2*10}= frac{-32}{20}=-1,6\a_2= frac{-11+21}{2*10}= frac{10}{20}=0,5\a_1neq sinx$
sinx=0,5
$x=(-1)^n,, frac{pi}{6},+,pi*n,nin mathbb{Z}$